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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Lagrange identity for polynomials and $ \delta $-codes of lengths $ 7t$ and $ 13t$

Author: C. H. Yang
Journal: Proc. Amer. Math. Soc. 88 (1983), 746-750
MSC: Primary 05B20; Secondary 05A19, 94B99
MathSciNet review: 702312
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Abstract: It is known that application of the Lagrange identity for polynomials (see [1]) is the key to composing four-symbol $ \delta $-codes of length $ (2s + 1)t$ for $ s = {2^a}{10^b}{26^c}$ and odd $ t \leqslant 59$ or $ t = {2^d}{10^e}{26^f} + 1$, where $ a$, $ b$, $ c$, $ d$, $ e$ and $ f$ are nonnegative integers. Applications of the Lagrange identity also lead to constructions of four-symbol $ \delta $-codes of length $ u$ for $ u = 7t$ or $ 13t$. Consequently, new families of Hadamard matrices of orders $ 4uw$ and $ 20uw$ can be constructed, where $ w$ is the order of Williamson matrices. Related topics on zero correlation codes are also discussed.

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PII: S 0002-9939(1983)0702312-0
Article copyright: © Copyright 1983 American Mathematical Society

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